There are many options available, if you wanted to take a nice day trip out of Budapest (I will hopefully over them all here). One of those nice options is undoubtedly the charming town of Gyor.
It is not the biggest of towns (maybe its a city IDK) and it can be seen in one whole day. The downtown has many well preserved buildings and they make for nice sights and nice photo opportunities. Some of the standout sights include the town hall, which is beautiful inside and out *see below*
The bridges and rivers, the citadel, the building which Napoleon himself stayed in, the eagle monument, and many other statues and monuments.
If you wanted to see the sights you could take a sightseeing train or simply meander around yourself at your own pace, the choice is yours.
If you become peckish for a bite to eat there are many restaurants at the town square, and with indoor and outdoor seating aplenty. We chose Szegedi Halászcsárda Győr for an enjoyable meal
https://goo.gl/maps/gCddQNiTcxkrifaq5
Want to go
There are frequent trains from Budapest Deli station. We got the passenger train which runs every hour direct, but there are multiple options available to you. I suggest checking the MAV train website for more information
Wanderlust Welshman 
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